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Number of nX3 0..1 arrays with no 1 equal to more than three of its king-move neighbors.
1

%I #6 Feb 28 2017 04:03:32

%S 8,57,324,2048,12771,79266,493671,3072417,19120172,119000389,

%T 740614274,4609310900,28686740079,178536045502,1111144834977,

%U 6915370693273,43038808688816,267858246154477,1667054510423628,10375154684003232

%N Number of nX3 0..1 arrays with no 1 equal to more than three of its king-move neighbors.

%C Column 3 of A282399.

%H R. H. Hardin, <a href="/A282394/b282394.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +5*a(n-2) +21*a(n-3) -29*a(n-4) +7*a(n-5) -61*a(n-6) +25*a(n-7) -62*a(n-8) +4*a(n-9).

%F Empirical: G.f.: -x*(8 +17*x -x^2 -25*x^3 -54*x^4 -36*x^5 -37*x^6 -58*x^7 +4*x^8) / ( -1 +5*x +5*x^2 +21*x^3 -29*x^4 +7*x^5 -61*x^6 +25*x^7 -62*x^8 +4*x^9 ). - _R. J. Mathar_, Feb 28 2017

%e Some solutions for n=4

%e ..1..1..1. .1..0..1. .0..0..0. .0..0..1. .0..0..0. .1..1..1. .0..0..0

%e ..1..0..0. .0..0..1. .0..1..0. .1..1..0. .0..0..0. .1..0..0. .0..0..0

%e ..0..1..1. .1..1..0. .0..1..1. .0..0..0. .0..0..0. .1..0..0. .0..0..1

%e ..0..1..0. .0..1..0. .0..0..0. .1..0..0. .0..0..1. .1..0..1. .0..1..1

%Y Cf. A282399.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2017